The possibility of a very small \({\tilde{\tau }_1} - \tilde{\chi }^0_{1}\)  mass difference opens up
the possibility that the \({\tilde{\tau }_1}\)  might have a long lifetime, as discussed
in the contexts of the CMSSM, NUHM1 and NUHM2 in [1]}.
This would occur if
\(m_{\tilde{\tau }_1} - m_{\tilde{\chi }^0_{1}} < m_\tau \) . As seen in the lower left panel of Fig. REF ,
the best-fit point has a mass difference \(\sim 20 \,\, \mathrm {GeV}\) ,
outside this range, but \(m_{\tilde{\tau }_1} - m_{\tilde{\chi }^0_{1}} < m_\tau \) 
is allowed with \(\Delta \chi ^2 \sim 1\) .
In Fig.  REF we analyze the lifetime of the \(\tilde{\tau }_{1}\) .
We see in the upper left panel of Fig. REF 
that there is essentially no \(\chi ^2\)  penalty for \(10^{-9}\)  s \( \lesssim \tau _{\tilde{\tau }_1} \lesssim 10^{-2}\)  s,
with lifetimes \(\sim 10^{-10}\)  s and \(\lesssim 10^3\)  s allowed with \(\Delta \chi ^2 \lesssim 1\) .
Distinguishing a separated-vertex signature at the LHC would be challenging for smaller
values of \(\tau _{\tilde{\tau }_1}\) , and there would be significant disruption of the successful
conventional Big Bang nucleosynthesis calculations for \(\tau _{\tilde{\tau }_1}\gtrsim 10^3\)  s [2]}.
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